Abstract

In variational imaging and other inverse problem modeling, regularisation plays a major role.In recent years, high order regularizers such as the mean curvature, the Gaussian curvature and Euler's elastica are increasingly studied and applied, and many impressive results over the widely-used gradient based models are reported.

Here we present some results from studying another class of high and non-integer order regularisers based on fractional order derivatives and focus on two aspects of this class of models:(i) theoretical analysis and advantages; (ii) efficient algorithms.We found that models with regularization by fractional order derivatives are convex in a suitable space and algorithms exploiting structured matrices can be employed to design efficient algorithms.Applications to restoration and registration are illustrated. This opens many opportunities to apply these regularisers to a wide class of imaging problems.

Ke Chen and J P Zhang, EPSRC Liverpool Centre for Mathematics in Healthcare,Centre for Mathematical Imaging Techniques,   and Department of Mathematical Sciences,The University of Liverpool,United Kingdom[ http://tinyurl.com/EPSRC-LCMH ]